This study introduces an innovative approach that employs Physics-Informed Neural Networks (PINNs) to address inverse problems in structural analysis. Specifically, this technique is applied to the 4th order partial differential equation (PDE) of the Euler–Bernoulli formulation to estimate beam displacement and identify structural parameters, including damping and elastic modulus. The methodology incorporates PDEs into the neural network’s loss function during training, ensuring it adheres to physics-based constraints. This approach simplifies complex structural analysis, even when explicit knowledge of boundary conditions is unavailable. Importantly, the method reliably captures structural behavior without resorting to synthetic noise in data — an experimental application is put forward to validate the framework. This study represents a pioneering effort in utilizing PINNs for inverse problems in structural analysis, offering potential inspiration for other fields. The characterization of damping, a typically challenging task, underscores the versatility of methodology. The strategy is initially assessed through numerical simulations utilizing data from a finite element solver and subsequently applied to experimental datasets. The presented methodology successfully identifies structural parameters using experimental data and validates its accuracy against state-of-the-art techniques. This work opens new possibilities in engineering problem-solving, positioning Physics-Informed Neural Networks as valuable tools in addressing practical challenges in structural analysis.

中文翻译：

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用于梁状结构模型参数识别的物理信息神经网络框架


本研究介绍了一种创新方法，该方法采用物理信息神经网络 （PINN） 来解决结构分析中的逆问题。具体来说，该技术应用于 Euler-Bernoulli 公式的 4 阶偏微分方程 （PDE），以估计梁位移并确定结构参数，包括阻尼和弹性模量。该方法在训练期间将 PDE 合并到神经网络的损失函数中，确保其遵守基于物理的约束。这种方法简化了复杂的结构分析，即使无法明确了解边界条件也是如此。重要的是，该方法可靠地捕获了结构行为，而无需在数据中使用合成噪声——提出了一个实验应用来验证该框架。这项研究代表了在结构分析中利用 PINN 解决逆问题的开创性努力，为其他领域提供了潜在的启发。阻尼的表征是一项典型的具有挑战性的任务，它强调了方法的多功能性。该策略最初通过利用有限元求解器的数据进行数值模拟进行评估，随后应用于实验数据集。所提出的方法使用实验数据成功地识别了结构参数，并根据最先进的技术验证了其准确性。这项工作为工程问题解决开辟了新的可能性，将物理信息神经网络定位为解决结构分析中实际挑战的宝贵工具。